We report the first observation of the decay B+-->psi(3770)K+ where the psi(3770) is reconstructed in the D0(-)D(0) and D+D- decay channels. The obtained branching fraction is B(B+-->psi(3770)K+)=(0.48+/-0.11+/-0.07)x10(-3). We have measured the branching fraction for the decay B+-->D0(-)D0K+ to be (1.17+/-0.21+/-0.15)x10(-3) and set a 90% confidence level upper limit of 0.90 x 10(-3) for the decay B+-->D+D-K+. We also present the results of a search for possible decays to D(-)D and D0(-)D(0)pi(0) of the recently observed X(3872) particle. The analysis is based on 88 fb(-1) of data collected at the Upsilon(4S) resonance by the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider.